Question

a stock broker has kept a daily record of the value of a particular stock over the years and finds that the prices of the stock form a normal distribution with a mean of $8.52 with a standard deviation of $2.38 the stock price beyond which 0.05 of the distribution fall is

Answer 1

The stock price beyond which 0.05 of the distribution fall is $12.44.

Explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean
`\mu` and standard deviation
`\sigma`, the zscore of a measure X is given by:

`Z = (X - \mu)/(\sigma)`

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Mean of $8.52 with a standard deviation of $2.38

This means that
`\mu = 8.52, \sigma = 2.38`

The stock price beyond which 0.05 of the distribution fall is

This is the 100 - 5 = 95th percentile, which is X when Z has a pvalue of 0.95. So X when Z = 1.645.

`Z = (X - \mu)/(\sigma)`

`1.645 = (X - 8.52)/(2.38)`

`X - 8.52 = 1.645*2.38`

`X = 12.44`

The stock price beyond which 0.05 of the distribution fall is $12.44.